To the best of our knowledge, Poisson approximation of (derived) Gibbs
processes is so far only discussed in very few articles in the
literature. In [1]} Stein's method (through
[2]}) is used to obtain bounds on the total
variation distance between a finite thinned Gibbs process and a
Poisson process.
However, as [1]} and the
examples given thereafter show, it is not easy to exploit these
bounds. (One needs to bound distances between densities
and empty space probabilities.)
In Theorem REF  and Theorem REF  below, we treat a
wider class of (scaled) thinned Gibbs processes and give very explicit
bounds on their total variation distance to a Poisson process. Our
proof exploits [2]} and is based on a coupling of
the thinned Gibbs process and its Palm version. This technique is
applied in [5]} to Poisson approximation of thinned Poisson
processes.
